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diff --git a/Master/texmf-dist/source/generic/xypic/xy2cell.doc b/Master/texmf-dist/source/generic/xypic/xy2cell.doc deleted file mode 100644 index 18bab67ac1f..00000000000 --- a/Master/texmf-dist/source/generic/xypic/xy2cell.doc +++ /dev/null @@ -1,1839 +0,0 @@ -%% $Id: xy2cell.doc,v 3.3 1996/12/18 14:21:23 ross Exp $ -%% -%% Xy-pic ``2-cell'' feature. -%% Copyright (c) 1993-1996 Ross Moore <ross@mpce.mq.edu.au> -%% -%% This file is part of the Xy-pic package for graphs and diagrams in TeX. -%% See the companion README and INSTALL files for further information. -%% Copyright (c) 1991-1996 Kristoffer H. Rose <krisrose@brics.dk> -%% -%% The Xy-pic package is free software; you can redistribute it and/or modify -%% it under the terms of the GNU General Public License as published by the -%% Free Software Foundation; either version 2 of the License, or (at your -%% option) any later version. -%% -%% The Xy-pic package is distributed in the hope that it will be useful, but -%% WITHOUT ANY WARRANTY; without even the implied warranty of MERCHANTABILITY -%% or FITNESS FOR A PARTICULAR PURPOSE. See the GNU General Public License -%% for more details. -%% -%% You should have received a copy of the GNU General Public License along -%% with this macro package; if not, write to the Free Software Foundation, -%% Inc., 675 Mass Ave, Cambridge, MA 02139, USA. -%% -\ifx\xyloaded\undefined \input xy \fi - -\xyprovide{2cell}{Two-cell feature}{\stripRCS$Revision: 3.3 $}% - {Ross Moore}{ross@mpce.mq.edu.au}% - {Mathematics Department, Macquarie University, NSW~2109, Australia} - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\noindent - This feature is designed to facilitate the typesetting of curved arrows, - either singly or in pairs, together with labels on each part and between. - The intended mathematical usage is for typesetting categorical ``2-cell'' - morphisms and ``pasting diagrams'', for which special features are provided. - These features also allow attractive non-mathematical effects. - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% -\paragraph*{Header:}\leavevmode -\DOCHEADER - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - The 2-cell feature makes use of facilities from the `curve' extension - which is therefore automatically loaded. - -\DOCMODE( -\xyrequire{curve}\xycatcodes -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsection{Typesetting 2-cells in Diagrams} - -\noindent -Categorical -``2-cell'' morphisms are used in the study of tensor categories and elsewhere. -The morphisms are displayed as a pair of curved arrows, symmetrically -placed, together with an orientation indicated by a short broad arrow, -or {\it Arrow}. Labels may be placed on all three components. - -\DOCMODE( -\message{two-cells,} -\DOCMODE) - -\UseAllTwocells - -\BUG: This document still uses version~2-style commmands, as described in -appendix~??g[:v2]. - -\xyrequire{v2}\xycatcodes - -\xymatrixcolsep{5pc}% -\xymatrixrowsep{2pc}% - -\begin{code} -\diagram -A\rtwocell^f_g &B\\ -\enddiagram -\end{code} -$$ \docode $$ -\displaycode - -\begin{code} -\diagram -A\ruppertwocell^f{\alpha} - \rlowertwocell_h{\beta} - \rto_(.35)g & B\\ -\enddiagram -\end{code} -$$ \docode $$ -\displaycode - -These categorical diagrams frequently -have a matrix-like layout, as with commutative diagrams. -To facilitate this there are control sequences of the form: -|\rtwocell| , |\ultwocell| , |\xtwocell| , \dots\ -analogous to the names defined in |xyv2| for use -in diagrams produced using |xymatrix|. -As this involves the definition of 21 new control sequences, many of which -may never be used, these are not defined immediately upon loading |xy2cell|. -Instead the user must first specify |\UseTwocells|. - -As in the second example above, just the upper or lower curved -arrow may be set using control sequences of the form -|\..uppertwocell| and |\..lowertwocell|. -These together with the |\..compositemap| family, in which -two abutting arrows are set with an empty object at the join, -allow for the construction of complicated ``pasting diagrams'' -(see figure ??[f.pasting] for an example). - -The following initialise the families of control sequences -for use in matrix diagrams. - -\begin{defs} - |\UseTwocells| &\quad two curves \cr - |\UseHalfTwocells| &\quad one curve \cr - |\UseCompositeMaps| &\quad 2 arrows, end-to-end \cr - |\UseAllTwocells| &\quad (all the above) \cr -\end{defs} - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\DOCMODE( -\xydef@\UseTwocells{\definesupermorphism{twocell}{% - \xy@{start of 2-cell}{\begingroup}% - \twocell@}} - -\xydef@\UseHalfTwocells{% - \definesupermorphism{uppertwocell}{% - \xy@{start of 2-cell}{\begingroup}% - \uppertwocell@}% - \definesupermorphism{lowertwocell}{% - \xy@{start of 2-cell}{\begingroup}% - \lowertwocell@}} - -\xydef@\UseCompositeMaps{\definesupermorphism{compositemap}{% - \xy@{start composite-map}{\begingroup}% - \compositemap@}} - -\xydef@\UseAllTwocells{% - \UseTwocells \UseHalfTwocells \UseCompositeMaps } -\DOCMODE) - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - The families of connections are defined using the utility macro\dots -% - |\definesupermorphism| -% - which defines control sequences for morphisms between - neighbouring cells, and next-to-neighbouring cells. - - More distant cells use |\xtwocell|, |\xcompositemap|, etc. - with <hop>s e.g. - |\xtwocell[1,3]| and |\xtwocell[llddd]|. - -\DOCMODE( -\xydef@\supermorphism#1[#2]#3{\def\afterMORPHISM{[#2]#3}#1} -\xydef@\afterMORPHISM{} - -\xydef@\definesupermorphism#1#2{% - \expandafter\def\csname x#1\endcsname{\supermorphism{#2}}% - \expandafter\def\csname u#1\endcsname{\supermorphism{#2}[-1,0]{}}% - \expandafter\def\csname d#1\endcsname{\supermorphism{#2}[1,0]{}}% - \expandafter\def\csname l#1\endcsname{\supermorphism{#2}[0,-1]{}}% - \expandafter\def\csname r#1\endcsname{\supermorphism{#2}[0,1]{}}% - \expandafter\def\csname uu#1\endcsname{\supermorphism{#2}[-2,0]{}}% - \expandafter\def\csname dd#1\endcsname{\supermorphism{#2}[2,0]{}}% - \expandafter\def\csname ll#1\endcsname{\supermorphism{#2}[0,-2]{}}% - \expandafter\def\csname rr#1\endcsname{\supermorphism{#2}[0,2]{}}% - \expandafter\def\csname ur#1\endcsname{\supermorphism{#2}[-1,1]{}}% - \expandafter\def\csname ul#1\endcsname{\supermorphism{#2}[-1,-1]{}}% - \expandafter\def\csname dr#1\endcsname{\supermorphism{#2}[1,1]{}}% - \expandafter\def\csname dl#1\endcsname{\supermorphism{#2}[1,-1]{}}% - \expandafter\def\csname uul#1\endcsname{\supermorphism{#2}[-2,-1]{}}% - \expandafter\def\csname uur#1\endcsname{\supermorphism{#2}[-2,1]{}}% - \expandafter\def\csname ull#1\endcsname{\supermorphism{#2}[-1,-2]{}}% - \expandafter\def\csname urr#1\endcsname{\supermorphism{#2}[-1,2]{}}% - \expandafter\def\csname ddl#1\endcsname{\supermorphism{#2}[2,-1]{}}% - \expandafter\def\csname ddr#1\endcsname{\supermorphism{#2}[2,1]{}}% - \expandafter\def\csname dll#1\endcsname{\supermorphism{#2}[1,-2]{}}% - \expandafter\def\csname drr#1\endcsname{\supermorphism{#2}[1,2]{}}% - \expandafter\def\csname uull#1\endcsname{\supermorphism{#2}[-2,-2]{}}% - \expandafter\def\csname uurr#1\endcsname{\supermorphism{#2}[-2,2]{}}% - \expandafter\def\csname ddll#1\endcsname{\supermorphism{#2}[2,-2]{}}% - \expandafter\def\csname ddrr#1\endcsname{\supermorphism{#2}[2,2]{}}} -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\bigskip - -Alternatively 2-cells can be set directly in \Xy-pictures without using the -matrix feature. In this case the above commands are not needed. This is -described in~\S??[standard]. - -Furthermore a new directional |\dir{=>}| can be used to -place an ``Arrow'' anywhere in a picture, -after the direction has been established appropriately. -It is used with all of the 2-cell types. - -\DOCMODE( -\newdir{=>}{!/5pt/\dir{=}!/2.5pt/\dir{=}*!/-5pt/\dir2{>}} - -\xydef@\arrowobject#1{\def\Arrowobject@{#1}} -\xydef@\Arrowobject@{\dir{=>}} -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -%{\obeylines\long\outer\gdef\Pastingexample{% -\begin{code} -\xymatrixrowsep{1.5pc} -\xymatrixcolsep{3pc} -\diagram - & & \relax\rtwocell<0>^{f_3^{}\;\;}{\omit} & \relax\ddtwocell<0>{\omit} - \drtwocell<0>^{\;\;f_4^{}}{<3>} - \ddrrtwocell<\omit>{<8>}\\ - & & & &\relax\drtwocell<0>^{\;\;f_5^{}}{\omit}\\ -A \uurrcompositemap<2>_{f_1^{}}^{f_2^{}}{<.5>} - \uurrlowertwocell<-6>{\omit}\relax - \drtwocell<0>_{g_1^{}\;}{\omit} - & & & \relax\urtwocell<0>{\omit} - & &\relax\rtwocell<0>^{f_6^{}\;}{\omit} - & \relax\rlowertwocell<-3>_{g_4^{}}{<-1>} - \rcompositemap<6>_{f_7^{}}^{f_8^{}}{\omit} & B \\ - & \relax\urrtwocell<0>{\omit} - \xcompositemap[-1,4]{}<-4.5>_{g_2^{}}^{g_3^{}}{\omit}\\ -\enddiagram -\end{code} - -\begin{figure*}[bt] -$$ \docode $$ -\caption{Pasting diagram.} -??=[f.pasting] -\end{figure*} - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\paragraph*{Default positions:} - - These set up default values for the parameters which - specify the position of each component - as well as the flags to indicate what type - of 2-cell is to be typeset. - -\begin{defs1} -\begin{tabular}{c l} - |\toks6| &position of control point, - normal to line $\overline{pc}$ at midpoint\\ - |\toks5| &position of central Arrow\\ - |\toks7| &position of |^| label\\ - |\toks8| &position of |_| label\\ - |\toks3| &flag for number of pieces... \\ - \quad |f| & \underline{f}ull: i.e. both curved arrows\\ - \quad |o| & \underline{o}ne: |\uppertwocell| or |\lowertwocell|\\ - \quad |t| & \underline{t}wo maps: |\compositemaps|\\ -\end{tabular} -\end{defs1} - -\noindent -|@| means to calculate from the value in |\toks6|, see |\tw@cell@@@|. - -\DOCMODE( -\xydef@\twocell@{\toks6={3.5}\toks5={@}\toks7={@}\toks8={@}\toks3={f}% - \tw@cell@ } -\xydef@\uppertwocell@{\toks6={7}\toks5={@}\toks7={@}\toks8={@}\toks3={o}% - \tw@cell@ } -\xydef@\lowertwocell@{\toks6={-7}\toks5={@}\toks7={@}\toks8={@}\toks3={o}% - \tw@cell@ } -\xydef@\compositemap@{\toks6={3.5}\toks5={@}\toks7={@}\toks8={@}\toks3={t}% - \tw@cell@ } -\DOCMODE) - - This collects together all the relevant data, and resolves the - default positions. - -\DOCMODE( -\xydef@\tw@cell@@@{% - \expandafter\ifx\the\toks6\omit\relax\toks6={}\else -% -% default position of label on upper arrow, -% relative to where it meets the perpendicular bisector -% - \expandafter\ifx\expandafter @\the\toks7\relax\expandafter\dimen@\the\toks6\p@ - \expandafter\if\the\toks3t\relax\dimen@=\p@ - \else\expandafter\if\the\toks3o\divide\dimen@\tw@ - \ifdim\dimen@<\z@ \dimen@ii-\p@ \advance\dimen@ii\dimen@ - \dimen@=\dimen@ii \else \dimen@\p@ \fi - \else\dimen@\p@ - \fi\fi - \edef\tmp@{\expandafter\removePT@\the\dimen@}% - \expandafter\toks\expandafter7\expandafter{\tmp@}\fi -% -% default position of label on lower arrow, -% relative to where it meets the perpendicular bisector -% - \expandafter\ifx\expandafter @\the\toks8\relax - \expandafter\dimen@\the\toks6\p@ - \expandafter\if\the\toks3t\relax\dimen@\p@ - \else\expandafter\if\the\toks3o\divide\dimen@\tw@ - \ifdim\dimen@<\z@ \dimen@ii-\p@ \advance\dimen@ii\dimen@ - \dimen@=\dimen@ii \else \dimen@\p@ \fi - \else\dimen@\p@ - \fi\fi - \edef\tmp@{\expandafter\removePT@\the\dimen@}% - \expandafter\toks\expandafter8\expandafter{\tmp@}\fi -% -% default position of the Arrow, relative to midpoint -% - \expandafter\ifx\expandafter @\the\toks5\relax - \expandafter\dimen@\the\toks6\p@ - \expandafter\if\the\toks3o\divide\dimen@ by-4\relax - \else\dimen@\z@\fi - \edef\tmp@{\expandafter\removePT@\the\dimen@}% - \expandafter\toks\expandafter5\expandafter{\tmp@}\fi - \fi -% -% possible modifications for module maps -% - \twocellmod@ -% -% pass all the parameters to |\twocell@@@@| -% - \expandafter\if\the\toks3t\relax -% -% composed maps: ^ : first map _ : second map -% - \edef\tmp@{.[\noexpand\twocell@@@@{\the\toks6}{\the\toks5}% - {\the\toks7}{\the\toks8}{\the\toks3}% - {\the\toks2}{\the\toks1}{\the\toks@}{\the\toks4}!!!].\afterMORPHISM}% - \else -% -% curved arrow(s) -% - \edef\tmp@{.[\noexpand\twocell@@@@{\the\toks6}{\the\toks5}% - {\the\toks7}{\the\toks8}{\the\toks3}% - {\the\toks1}{\the\toks2}{\the\toks@}{\the\toks4}!!!].\afterMORPHISM}% - \fi - \toks@={\endgroup}% - \expandafter\def\expandafter\next@\expandafter{% - \expandafter\def\expandafter\twocellhead@\expandafter{\twocellhead@}}% - \expandafter\addtotoks@\expandafter{\next@}% - \expandafter\def\expandafter\next@\expandafter{% - \expandafter\def\expandafter\twocelltail@\expandafter{\twocelltail@}}% - \expandafter\addtotoks@\expandafter{\next@}% - \expandafter\addtotoks@\expandafter{\expandafter\twocellPATH\tmp@}% - \the\toks@ }% -\DOCMODE) - - See below for the possible forms of |\twocellPATH|. - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -Labels are placed labels on the upper and lower arrows, -more correctly `anti-clockwise' and `clockwise', using |^| and |_|. -These are entirely optional with the following token, or grouping, giving -the contents of the label. When used with -|\..compositemap| the |^| and |_| specify -labels for the first and second arrows, respectively. - -\DOCMODE( -\xydef@\twocellstyle{\scriptstyle} - -\xydef@\droptwocelllabel@#1{\xyFN@\droptwocelllabel@@#1@!} -\xydef@\droptwocelllabel@@{% - \ifx*\next\DN@*{\droptwocelldrop@}% - \else\DN@##1@!{\droptwocelltext@{##1}}% - \fi \next@ } - -{\xyuncatcodes \gdef\next#1{\drop+!C{\twocellstyle #1}}} -\xylet@\droptwocelltext@=\next - -\xydef@\droptwocelldrop@#1@!{\bgroup \let\xy@=\oxy@ - \let\objectstyle=\twocellstyle \drop#1{}% - \edef\tmp@{\egroup \X@min=\the\X@min \X@max=\the\X@max - \Y@min=\the\Y@min \Y@max=\the\Y@max}\tmp@ } -\DOCMODE) - -Normally the label is balanced text, set -in \TeX's math mode, with |\twocellstyle| setting the style. -The default definition is given by \dots - -|\def\twocellstyle{\scriptstyle}| - -\noindent -This can be altered using |\def| in versions of \TeX\ -or |\redefine| in \LaTeX. -However labels are not restricted to being simply text boxes. -Any effect obtainable using the \Xy-pic kernel language can be set -within an |\xybox| and used as a label. Alternatively if the first -character in the label is |*| then the label is set as an -\Xy-pic <object>, as if with |\drop<object>| or |*<object>| in -the kernel language. The current direction is tangential to -the curved arrows. Extra braces are needed to get a |*| as the label, -as in |^{{{*}}}| or |_{{}*}|. - -The position of a label normal to the tangential direction -can also be altered by {\em nudging} (see below). -Although it is possible to specify multiple labels, -only the last usage of each of |^| and |_| is actually set, -previous specifications being ignored. - -Similarly a label for the central Arrow must be given, -after the other labels, by enclosing it within braces |{...}|. -An empty group |{}| gives an empty label; this is necessary -to avoid misinterpretation of subsequent tokens. As above if the -first character is |*| then the label is set as an \XY-pic <object>, -the current direction being along the Arrow. - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\paragraph*{Parsing:} - - Open a new group so the following registers can be used locally... - |\toks@=\toks0|, |\toks1|, ..., |\toks8| - the final parameter set is stored briefly in |\tmp@| before being used. - - OPTIONS: -\begin{defs1} -\begin{tabular}{c c l} - && spaces are ignored \\ - |<| & |<num>| &determines position of curves control point\\ - & |<0>| &uses a single solid line,\\ - & |<\omit>| &causes only the central Arrow (with label) to be set\\ -\noalign{\smallskip} - |\omit| &&omits the curved arrows, but allows their labels\\ - |^| &&place ``above'' label (more correctly ``anti-clockwise'')\\ - |_| &&place ``below'' label (more correctly ``clockwise'')\\ - |~'| &&change the arrowhead \\ - |~`| &&place/change the arrowtail\\ -\end{tabular} -\end{defs1} - - Label data e.g. |^{#1}| |_{#1}| - is stored temporarily in |\toks@| then passed via |\tw@@cell@@| - to |\tw@cell@@| for further parsing, as: |\the\toks@ @| - - |~'| and |~`| change the values of |\twocellhead@| and |\twocelltail@| - Normally |\twocelltail@| is |{}|, so |~`| also changes a flag to - indicate that |\twocelltail@| is indeed required. - - When the next token is a grouping |{...}| - then it gives the label for the central Arrow. - No other label specifications may follow. - - - Default head and tail ornaments... - -\DOCMODE( -\xydef@\twocellhead#1{\def\twocellhead@{#1}} -\xydef@\twocelltail#1{\def\twocelltail@{#1}} -\xydef@\twocellhead@{\dir{>}} -\xydef@\twocelltail@{} -\DOCMODE) - - clear |\toks..| registers for the new connection labels. - -\DOCMODE( -\xywarnifdefined\twocellmod@ -\xydef@\tw@cell@{\begingroup - \toks@={{}}\toks1={{}}\toks2={{}}\toks4={{}}% - \def\twocellmod@{}\xyFN@\tw@@cell@}% - -\xydef@\tw@@cell@{% - \ifx\space@\next\expandafter\DN@\space{\xyFN@\tw@@cell@}% - \else\ifx\bgroup\next \let\next@=\toks@\afterassignment\tw@@cell@@ - \else\ifx ^\next \DN@^##1{\toks@={##1}\nudgepos@71\tw@@cell@}% - \else\ifx _\next \DN@_##1{\toks@={##1}\nudgepos@82\tw@@cell@}% - \else\addLT@\ifx \next \addGT@{\addLT@\DN@##1}{% - \toks6={##1}\ifx\omit##1\relax\toks3={t}\toks5={0}\fi\xyFN@\tw@@cell@}% - \else\ifx\omit\next \DN@\omit{\omitarrows@\xyFN@\tw@@cell@}% - \else\ifx~\next \DN@~{\xyFN@\whichCurveObject@}% - \else \DN@{\xyFN@\tw@cell@@\empty @}% - \fi\fi\fi\fi\fi\fi\fi% - \next@ } - -\xydef@\whichCurveObject@{% - \ifx\space@\next\expandafter\DN@\space{\xyFN@\whichCurveObject@}% - \else\ifx\next^\DN@^##1{\xy@{~^{##1}}{\uppercurveobject{##1}}\xyFN@\tw@@cell@}% - \else\ifx\next_\DN@_##1{\xy@{~_{##1}}{\lowercurveobject{##1}}\xyFN@\tw@@cell@}% - \else\addRQ@\ifx\next \addRQ@\DN@##1{% - \xy@{~'{##1}}{\def\twocellhead@{##1}}\xyFN@\tw@@cell@}% - \else\addLQ@\ifx\next \addLQ@\DN@##1{% - \xy@{~`{##1}}{\def\twocelltail@{##1}}\xyFN@\tw@@cell@}% - \else\ifx!\next \DN@!{\xyFN@\checkmodmap@}% - \else\ifx\next\bgroup\DN@##1{\xy@{~{##1}}{\curveobject{##1}}\xyFN@\tw@@cell@}% - \else\DN@##1{\xy@{~##1}{\curveobject{##1}}\xyFN@\tw@@cell@}% - \fi\fi\fi\fi \fi\fi\fi - \next@ } - -\xydef@\checkmodmap@{% - \ifx\space@\next\expandafter\DN@\space{\xyFN@\checkmodmap@}% - \else \def\twocellmod@{\modmap@}% - \ifx\next!\DN@!##1{% - \xy@{~!!{##1}}{\def\modmapobject@{##1}}\xyFN@\tw@@cell@}% - \else \DN@{\xyFN@\tw@@cell@}\fi - \fi \next@ } -\DOCMODE) - - With no arrows, still allow labels: - default positions are at $0$, $+X$, $-X$, with $X=${\em default value}. - These values are altered by ``nudging''. - -\DOCMODE( -\xydef@\omitarrows@{\toks5={0}\toks6={}\toks7={0}\toks8={0}} -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{figure*}[tp] -\begin{syntax} -% -<twocell> - &\iss & <2-cell><switches><Arrow> - & typeset <2-cell> with the <switches> and <Arrow> -\cr -\noalign{\smallskip} -% -<2-cell> &\iss & |\..twocell| - & typeset two curved arrows -\cr - &\orr & |\..uppertwocell| - & typeset upper curved arrow only -\cr - &\orr & |\..lowertwocell| - & typeset lower curved arrow only -\cr - &\orr & |\..compositemap| - & use consecutive straight arrows -\cr -\noalign{\smallskip} -% -<Arrow> &\iss & |{|<tok><text>|}| - & specifies orientation and label -\cr - &\orr & |{|<nudge><text>|}| - & adjust position, use default orientation -\cr - &\orr & |{|<text>|}| - & use default position and orientation -\cr - &\orr & |{|<tok>*<object>|}| - & use <object> as the label -\cr - &\orr & |{|<nudge>*<object>|}| \orr |{|*<object>|}| -\cr -\noalign{\smallskip} -% -<tok> &\iss & |^| \orr |_| \orr |=| - & oriented anti-/clockwise/equality -\cr - &\orr & |\omit| - & no Arrow, default is clockwise -\cr - &\orr & |`| \orr |'| \orr |"| \orr |!| - & no Arrow; tips on two curved arrows as:\\ - anti-/clockwise/double-headed/none -\cr -\noalign{\smallskip} -% -<switches> &\iss & <switch><switches> - & list of optional modifications -\cr -\noalign{\smallskip} -% -<switch> &\iss & <empty> - & use defaults -\cr -% - &\orr & |^| <label> - & place <label> on the upper arrow -\cr - &\orr & |_| <label> - & place <label> on the lower arrow -\cr - &\orr & <nudge> - & set the curvature, based on <nudge> value -\cr - &\orr & |\omit| - & do not set the curved arrows -\cr - &\orr & \ |!| - & place |\modmapobject| midway along arrows -\cr - &\orr & |~| <what> |{| <object> |}| - & use <object> in place specified by <what> -\cr -\noalign{\smallskip} -% -<what> &\iss & <empty> - & set curves using the specified <object> -\cr - &\orr & |^| \orr |_| - & use <object> with upper/lower curve -\cr - &\orr & |`| \orr |'| - & use <object> for arrow head/tail -\cr -% -\noalign{\medskip} -% -<label> &\iss & <text>\ \orr\ <nudge> <text> - & set <text>, displaced by <nudge> -\cr - &\orr & *<object>\ \orr\ <nudge>*<object> - & set <object>, displaced by <nudge> -\cr -\noalign{\smallskip} -% -<nudge> &\iss & |<|<number>|>| & use <number> in an appropriate way, - \eg, to position object or label along a fixed axis -\cr - &\orr & |<\omit>| & do not typeset the object/label -\cr -% -\end{syntax} -\caption{\protect<twocell\protect>s} -??=[f.twocell] -\end{figure*} - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsection{Standard Options}??=[Arrow] -The orientation of the central Arrow may be reversed, -turned into an equality, or omitted altogether. -In each case a label may still be specified, so in effect the -Arrow may be replaced by anything at all. - -These effects are specified by the first token in the central label, -which thus has the form: |{|<tok><label>|}| -where <tok> may be one of \dots - -\begin{defs1} -\begin{tabular}{ c l } - |_| & Arrow points clockwise \cr - |^| & Arrow points anti-clockwise \cr - |=| & no tip, denotes equality \cr -|\omit|& no Arrow at all. \cr -\end{tabular} -\end{defs1} - -\noindent -When none of these occurs then the default of |_| is assumed. -If the label itself starts with one of these characters then -specify |_| explicitly, or enclose the label within a group |{...}|. -See {\em Extra Options~1}, for more values of <tok>. -Also note that |*| has a special role when used as the first character; -however it is considered to be part of the <label>, see above. - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - OPTIONS for the central Arrow: - -\begin{defs}{c l} - & ignore spaces\cr - |^| & points anti-clockwise\cr - |_| & points clockwise (default)\cr - |=| & no |\Tip|, equality\cr - |\omit|& no Arrow at all, just squine(s) or composed arrows\cr - |'| & no Arrow, opposite squine reversed\cr - |`| & no Arrow, forward squine reversed\cr - |"| & no Arrow, tips on both ends\cr - |!| & no Arrow, no tips on squines\cr -\end{defs} - - the position of the Arrow is determined by ``nudging'' (see below) - e.g. - |{^<num>label}|, where the actual dimen is |<num>\xydashl@| - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{code} -\xymatrixcolsep{4pc} -\xymatrixrowsep{1pc} -\diagram -A \rtwocell{_\alpha} & B \rtwocell{^\beta} & -C \rtwocell{=\gamma} & D \rtwocell{\omit\Psi} & E \\ -\enddiagram -\end{code} -$$ \docode $$ -\displaycode - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\paragraph{Parsing of the Arrow's label} - -\DOCMODE( -\xydef@\tw@@cell@@{\expandafter\xyFN@\expandafter\tw@cell@@\the\toks@ @} - -\xydef@\tw@cell@@{\ifx \space@\next\expandafter\DN@\space{\xyFN@\tw@cell@@}% - \else\ifx ^\next - \DN@^##1@{\toks@={##1}\toks4={^}\nudgepos@50\tw@cell@@@}% - \else\addEQ@\ifx\next - \addEQ@\DN@##1@{\toks@={##1}\toks4={=}\nudgepos@50\tw@cell@@@}% - \else\ifx _\next - \DN@_##1@{\toks@={##1}\toks4={_}\nudgepos@50\tw@cell@@@}% - \else\addLT@\ifx \next - \DN@##1@{\toks@={##1}\toks4={_}\nudgepos@50\tw@cell@@@}% - \else\ifx\omit\next \DN@\omit##1@{\toks4={@}\toks@={##1}\tw@cell@@@}% - \else\addRQ@\ifx\next \addRQ@\DN@##1@{\toks4={@}\toks3={/}\toks@={##1}% - \nudgepos@50\tw@cell@@@}% - \else\addLQ@\ifx\next \addLQ@\DN@##1@{\toks4={@}\toks3={b}\toks@={##1}% - \nudgepos@50\tw@cell@@@}% - \else\ifx"\next \DN@"##1@{\toks4={@}\toks3={B}\toks@={##1}% - \nudgepos@50\tw@cell@@@}% - \else\ifx!\next \DN@!##1@{\toks4={@}\toks3={@}\toks@={##1}% - \nudgepos@50\tw@cell@@@}% - \else\ifx\next\empty\DN@##1@{\toks@={{}}\toks4={_}\tw@cell@@@}% - \else\DN@##1@{\toks@={##1}\toks4={_}\tw@cell@@@}% - \fi\fi\fi\fi\fi\fi\fi\fi\fi\fi\fi \next@ } -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsection{Nudging} -Positions of all labels may be adjusted, -as can the amount of curvature for the curved arrows. -The way this is done is by specifying a ``nudge'' factor <num> -at the beginning of the label. -Here <num> is a number which specifies the actual position of the label -in units of |\xydashl@| (the length of a single dash, normally 5pt) -except with |\..compositemap|, see below. -Movement is constrained to the perpendicular bisector -of the line $\overline{cp}$. -When nudging the label for the central Arrow -it is the whole Arrow which is moved, along with its label. - -Curvature of the arrows themselves is altered by -a nudge of the form |\..twocell|<num>.... -The separation of the arrows, along the bisector, -is set to be <num>|\xydashl@|. -When <num> is zero, that is |\..twocell<0>...|, -the result is a single straight arrow, -its mid-point being the origin for nudging labels. -A negative value for <num> is also acceptable; -but check the orientation on the Arrow -and which of |^| and |_| correspond to which component. - -The origin for nudging labels is where the arrow -crosses the bisector. Positive nudges move -the label outwards while negative nudges move towards $\overline{pc}$ -and possibly beyond. -The default position of a label is on the outside, with edge at the origin. - -The origin for nudging the Arrow is at the midpoint of $\overline{pc}$. -A positive nudge moves in the clockwise direction. -This will be the direction of the arrowhead, -unless it has been reversed using |^|. - -\smallskip - -Labels on a |\..compositemap| are placed relative to the midpoint -of the component arrows. Nudges are in units of 1pt. -Movement is in the usual \Xy-pic {\em above} and {\em below} directions, -such that a positive nudge is always outside the triangle formed -by the arrows and line $\overline{pc}$. - -\medskip - -The special nudge value |<\omit>| typesets just the Arrow, -omitting the curved arrows entirely. -When used with labels, the nudge value |<\omit>| causes the following label -to be ignored. - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{exercise} -Give code to typeset figure ??[f.pasting]. - -\noindent -Such code is relatively straight-forward, using ``nudging'' -and |\omit| to help position the arrows, curves and Arrows. -It also uses an {\em excursion}, -as described below in the subsection {\em Extra Options~3}. - -% code from the earlier ``Pasting diagram'' example. -%\Pastingexample\gdef\Pastingexample{}% -% -\begin{code} -\xymatrixrowsep{1.5pc} -\xymatrixcolsep{3pc} -\diagram - &&\relax\rtwocell<0>^{f_3^{}\;\;}{\omit} - &\relax\ddtwocell<0>{\omit} - \drtwocell<0>^{\;\;f_4^{}}{<3>} - \ddrrtwocell<\omit>{<8>}\\ -&&&&\relax\drtwocell<0>^{\;\;f_5^{}}{\omit}\\ -A \uurrlowertwocell<-6>{\omit}\relax -\uurrcompositemap<2>_{f_1^{}}^{f_2^{}}{<.5>} - \drtwocell<0>_{g_1^{}\;}{\omit} - &&&\relax\urtwocell<0>{\omit} - &&\relax\rtwocell<0>^{f_6^{}\;}{\omit} - &\relax\rlowertwocell<-3>_{g_4^{}}{<-1>} - \rcompositemap<6>_{f_7^{}}^{f_8^{}}{\omit} - & B \\ - &\relax\urrtwocell<0>{\omit} - \xcompositemap[-1,4]{}% - <-4.5>_{g_2^{}}^{g_3^{}}{\omit}\\ -\enddiagram -\end{code} - -\answertext{Here is the code used to typeset the {\em pasting diagram} in -figure~??g[xy2cell.doc:f.pasting].} -\answercode -\answertext\displaycode - -\answertext{\smallskip\noindent -For the straight arrows, it would have been simpler to use |\..to| -provided |xyarrow| has been loaded. Instead |\..twocell<0>...{\omit}| -was used to illustrate the versatility of nudging and |\omit|; -thus |xy2cell| can completely handle a wide range of diagrams, -without requiring |xyarrow|. Note also the use of |\relax| at the start -of each new cell, to avoid premature expansion of a complicated macro, -which can upset the compiling mechanism.} -\end{exercise} - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\paragraph{NUDGE } position of labels - -\DOCMODE( -\xywarnifdefined\whichnudge -\xywarnifdefined\whichinfo -\xywarnifdefined\afternudge -\xydef@\nudgepos@#1#2#3{\def\whichnudge{\toks#1}\def\whichinfo{\toks#2}% - \def\afternudge{#3}\expandafter\xyFN@\expandafter\nudgepos@@\the\toks@ @} -\DOCMODE) - -\begin{defs1} -\begin{tabular}{c l} - |#1| & which token register to store nudge amount\cr - |#2| & which token register to store label\cr - |#3| & what to do next, after parsing \cr -\end{tabular} -\end{defs1} - -\paragraph{Parsing: } -% - <num><label>|@|, <num> = nudge amount, as multiple of |\xydashl@|. - -\DOCMODE( -\xydef@\nudgepos@@{\ifx \space@\next\expandafter\DN@\space{\xyFN@\nudgepos@}% - \else\addLT@\ifx \next - \addGT@{\addLT@\DN@##1}##2@{% - \ifx\omit##1\relax\whichnudge={0}\whichinfo={}% - \else\whichnudge={##1}\whichinfo={##2}\fi\xyFN@\afternudge}% - \else \DN@##1@{\whichinfo={##1}\xyFN@\afternudge}% - \fi\fi \next@ } -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsection{Extra Options} -The following features are useful in non-mathematical applications. - -\subsubsection*{1. no Arrow} -This is determined by special values for <tok> as the -first (or only) character in the central label, as in the above -description of the standard switches. - -\begin{defs1} -\begin{tabular}{c l} - |'| & arrowheads pointing clockwise;\cr - |`| & arrowheads pointing anti-clockwise;\cr - |"| & arrow tips on both ends;\cr - |!| & no tips at all.\cr -\end{tabular} -\end{defs1} - -\noindent -The central Arrow is omitted, leaving symmetrically placed -curved connections with arrowheads at the specified ends. -A label can be placed where the Arrow would have been. - -If a special arrowhead is specified using |~'{..}| -(see Extra Options~2, below) -then this will be used instead of the standard |\dir{>}|. - -\ifx\undefined\mathbf\def\mathbf{\boldmath}\fi -\begin{code} -\xymatrixcolsep{5pc} -\diagram - \relax\txt{Clouds }\rtwocell<10> - _{\hbox{\tiny evaporation }} - ^{\hbox{\tiny precipitation }} -{'{\mathbf{H_2 O}}} -&\relax\txt{Oceans}\\ -\enddiagram -\end{code} -$$ \docode $$ -\displaycode - -\begin{code} -\xymatrixcolsep{5pc} -\diagram -\relax\txt{\llap{Math}ematics }\rtwocell -_{\hbox{\tiny experiment }} -^{\hbox{\tiny theory }}{"} -& \relax\txt{Physics} \\ -\enddiagram -\end{code} -$$ \docode $$ -\displaycode - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsubsection*{2. Changing Tips and Module Maps } -The following commands are provided for specifying the <object> -to be used when typesetting various parts of the twocells. - -\medskip -\noindent -\begin{tabular}{l c} -\noalign{\hrule} -\noalign{\smallskip} -{\em command} \hfill & {\em default} \cr -\noalign{\smallskip} -\noalign{\hrule} -\noalign{\smallskip} - |\modmapobject{|<object>|}| & |\dir{|$\vert$|}| \cr - |\twocellhead{|<object>|}| & |\dir{>}| \cr - |\twocelltail{|<object>|}| & |\dir{}| \cr - |\arrowobject{|<object>|}| & |\dir{=>}| \cr -\noalign{\smallskip} - |\curveobject{|<object>|}| & \cr - |\uppercurveobject{|<object>|}| & |{}| \cr - |\lowercurveobject{|<object>|}| & |{}| \cr -\noalign{\smallskip} -\noalign{\hrule} -\end{tabular} -\medskip - - -These commands set the object to be used for all subsequent -2-cells at the same level of \TeX\ grouping. -|\curveobject| specifies both of the upper- and lower-curve objects. -For some of these there is also a way to change the object for the -current 2-cell only. -This requires a |~|-<switch> which is described below, -except for the |\..curveobject| types, which are discussed in -{\em Extra Options~4}. - -\medskip - -These effects are specified by placing switches -after the |\..twocell| control sequence, -\eg\ |\rtwocell| {\em switches\/} {\em labels\/}\dots~. -Each switch is either a single token <tok>, or a -|~|<tok> with a single argument: |~|<tok>|{|{\em arg\/}|}|. -Possibilities are listed in the following table, -in which |{..}| denotes the need for an argument. - -\begin{defs1} -\begin{tabular}{c l} - |\omit| & no arrows, Arrow and label only;\cr - |!| & place module-map indicator;\cr -|~'{..}| & change arrow-head to |{..}|;\cr -|~`{..}| & place/change tail on arrow(s);\cr -|~{..}| & change object used to set curves;\cr -|~^{..}| & use object |{..}| to set upper curve;\cr -|~_{..}| & use object |{..}| to set lower curve;\cr -\end{tabular} -\end{defs1} - -\noindent -Here we discuss the use of |!|, |~'|, |~`| and |\omit|. -The description of |~^|, |~_| and |~{..}| is given in {\em Extra Options~4}. - -\medskip -The default module map indicator places a single -dash crossing the arrow at right-angles, -located roughly midway along the actual printed portion of the arrow, -whether curved or straight. -This takes into account the sizes of the objects being connected, -thereby giving an aesthetic result when these sizes differ markedly. -This also works with |\..compositemap| where an indicator is placed -on each arrow. The actual object can be changed using |\modmapobject|. - -\medskip -Any of the standard \Xy-pic tips may be used for arrow-heads. -This is done using |~'{..}|, -for example |~'{\dir{>>}}| gives double-headed arrows. -Similarly |~`{..}| can be used to place an arrow-tail. -Normally the arrow-tail is {}, so is not placed; -but if a non-empty tail has been specified then it will -be placed, using |\drop|. -No guarantee is offered for the desired result being obtained -when an arrow-tail is mixed with the features of {\em Extra Options~1}. - -\begin{code} -\modmapobject{\objectbox{\otimes}} -\xymatrixcolsep{5pc} -\diagram -P\rtwocell~!~'{\dir{>>}}~`{\dir{|}} - ^{<1.5>M}_{<1.5>M'}{=f} & S \\ -\enddiagram -\end{code} -$$ \docode $$ -\displaycode - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - switch for module maps... - ...places decoration called |\modmapobject| half way along arrows - -\DOCMODE( -\xydef@\modmap@{% - \expandafter\ifx\the\toks4@\toks4={!}% - \else\expandafter\ifx\the\toks4=\toks4={H}% - \else\expandafter\ifx\the\toks4^\toks4={A}% - \else\expandafter\ifx\the\toks4_\toks4={V}\fi\fi\fi\fi - \expandafter\DN@\expandafter{\the\toks6}% - \ifx\next@\empty\relax\else\expandafter\moddefs@\fi} -\DOCMODE) - - also adjust curvature and label positions - -\DOCMODE( -\xydef@\moddefs@{% - \expandafter\dimen@\the\toks6\p@ - \ifdim\dimen@=\z@\relax - \expandafter\dimen@\the\toks7\p@ - \ifdim\dimen@<\z@\advance\dimen@.5\p@\else\advance\dimen@-.5\p@\fi - \edef\tmp@{\noexpand\toks7={\expandafter\removePT@\the\dimen@}}\tmp@ - \expandafter\dimen@\the\toks8\p@ - \ifdim\dimen@<\z@\advance\dimen@-.5\p@\else\advance\dimen@.5\p@\fi - \expandafter\ifx\the\toks3t\advance\dimen@-1\p@\fi - \edef\tmp@{\noexpand\toks8={\expandafter\removePT@\the\dimen@}}\tmp@ - \else - \ifdim\dimen@<\z@\advance\dimen@-.5\p@\else\advance\dimen@.5\p@\fi - \edef\tmp@{\noexpand\toks6={\expandafter\removePT@\the\dimen@}}\tmp@ -% \expandafter\dimen@\the\toks5\p@ -% \ifdim\dimen@<\z@\advance\dimen@-.5\p@\else\advance\dimen@.5\p@\fi -% \edef\tmp@{\noexpand\toks5={\expandafter\removePT@\the\dimen@}}\tmp@ - \expandafter\dimen@\the\toks7\p@ - \ifdim\dimen@<\z@\advance\dimen@-.5\p@\else\advance\dimen@.5\p@\fi - \expandafter\ifx\the\toks3t\advance\dimen@-2\p@\fi - \edef\tmp@{\noexpand\toks7={\expandafter\removePT@\the\dimen@}}\tmp@ - \expandafter\dimen@\the\toks8\p@ - \ifdim\dimen@<\z@\advance\dimen@-.5\p@\else\advance\dimen@.5\p@\fi - \expandafter\ifx\the\toks3t\advance\dimen@-2\p@\fi - \edef\tmp@{\noexpand\toks8={\expandafter\removePT@\the\dimen@}}\tmp@ - \fi }% - -%\def\moddefs@{} -\DOCMODE) - - default object is |\stop|, user can change this with |\modmapobject#1| - -\DOCMODE( -\xydef@\modmapobject#1{\def\modmapobject@{#1}} -\xydef@\modmapobject@{\dir{|}} -\xydef@\@modmapobject@{{\if\@mod@\relax\expandafter\empty - \else\expandafter\modmapobject@\fi}} -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsubsection*{3. Excursions} -Syntax for |\xcompositemap| and |\x..twocell| types -is a little different to -what might be expected from that for |\xto|, |\xline|, etc. -For example, -% -\begin{defs1} -|\xtwocell[|<hop>|]{|<displace>|}...| -\end{defs1} -% -\noindent -connects to the <pos> displaced by <displace> from -the relative cell location specified by <hop>. -The displacement can be any string of valid \Xy-pic commands, -but they must be enclosed within a group |{...}|. -When the cell location is the target, -a~null grouping |{}| {\em must} be given. - -When used with the |<\omit>| nudge, such excursions allow a labelled Arrow -to be placed anywhere within an \Xy-pic diagram; -furthermore the Arrow can be oriented to point in any direction. - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\DOCMODE( -\xydef@\curveobject#1{\def\ucurveObject@{~*#1}\def\dcurveObject@{~*#1}} -\xydef@\uppercurveobject#1{\def\ucurveObject@{~*#1}} -\xydef@\lowercurveobject#1{\def\dcurveObject@{~*#1}} -\xydef@\ucurveObject@{} -\xydef@\dcurveObject@{} -\DOCMODE) - -The empty object gives the default of closely spaced tiny dots, -resulting in a ``smooth'' curve. - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -The following macro is used in conjunction with compiling diagrams, -to include the global parameters in the compiled file. - -\DOCMODE( -\xydef@\savetwocellobjects{% - \xy@{twocell objects}{% - \expandafter\uppercurveobject\expandafter{\ucurveObject@}% - \expandafter\lowercurveobject\expandafter{\dcurveObject@}% - \expandafter\modmapobject\expandafter{\modmapobject@}% - \expandafter\twocellhead\expandafter{\twocellhead@}% - \expandafter\twocelltail\expandafter{\twocelltail@}% - \expandafter\arrowobject\expandafter{Arrowobject@}% - }} -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsubsection*{4. Fancy curves} -By specifying |\curveobject| an arbitrary object may be used to -construct the curved arrows. Indeed with a -|\..twocell| different objects can be used with -the upper and lower curves by specifying -|\uppercurveobject| and |\lowercurveobject|. - -These specifications apply to all 2-cells subsequently constructed at -the same level of \TeX\ grouping. -Alternatively using a |~|-switch, as in {\em Extra Options~2}, -allows such a specification for a single 2-cell or curved part. - -Objects used to construct curves can be of two types. -Either a single <object> is set once, with copies placed along the curve. -Alternatively a directional object can be aligned with -the tangent along the curve. In this case use a specification takes the -form: - -|\curveobject{|<spacer>|~**|<object>|}|. - -\noindent -Here <spacer> may be any <object> of non-zero size. -Typically it is empty space, \eg\ |+|<dimen>|{}|. - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{exercise} -Give code to typeset the following diagrams. - -\begin{code} -{\uppercurveobject{{?}} - \lowercurveobject{{\circ}} -\xymatrixcolsep{5pc} -\xymatrixrowsep{2pc} -\diagram - \relax\txt{ FUn }\rtwocell<8>{!\&} - & \relax\txt{ gaMES } - \enddiagram} -\end{code} -$$\docode$$ - -\answertext{Here is the code -used by the author to set the first diagram.} -\answercode -\answertext\displaycode - -\begin{code} -\xymatrixcolsep{2.5pc} -\xymatrixrowsep{4pc} -\diagram - \relax\txt<1.5cm>{\bf Ground State} - \rrtwocell<12>~^{+{}~**!/-2.5pt/\dir{>}} - ~_{++{}~**!/5pt/\dir{<<}} - ^{<1.5>\txt{\small continuous power}} - _{<1.5>\txt{\small pulsed emission}}{!} -& \relax\;\; N\!i\,C\!d\;\; \Circled -& \relax\txt<1.50cm>{\bf Excited State} -\enddiagram -\end{code} -$$\docode$$ - -\answertext{Here is the code -used for the second diagram.} -\answercode -\answertext\displaycode - -\end{exercise} - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsection{After Parsing...} - - Values for |\twocellPATH|, depends on the mode of picture/diagram - as to whether the |@c| and |@p| are known yet, or still have - to be read. - -\DOCMODE( -\xydef@\twocell@path.[#1].{% - \expandafter\ifx\csname Q@@c\endcsname\relax - \DN@{\enter@{\cfromthec@ \pfromthep@ \basefromthebase@}% - \xy@{}{\expandafter\edef\csname Q@@\endcsname{\cfromthec@}}% - \afterPOS{\xy@{}% - {\expandafter\edef\csname Q@@c\endcsname{\cfromthec@}}% - \xy@{}% - {\cfromid@{@}\expandafter\edef\csname Q@@p\endcsname{\cfromthec@}}% - \xy@{twocell #1}{#1}\leave@\aftertwoCELL};p,}% - \else - \DN@{\enter@{\cfromthec@ \pfromthep@ \basefromthebase@}% - \xy@{twocell #1}{#1}\leave@\aftertwoCELL}% - \fi \next@ } - -\xydef@\twocellpath.[#1].{% - \expandafter\edef\csname Q@@p\endcsname{\cfromthec@}% - \xy@{}{\enter@{\pfromthep@}}% - \xy@{}{\enter@{\cfromthec@ \pfromthep@ \basefromthebase@}% - \enter@{\pfromthec@}}% - \afterPOS{\xy@{}{\leave@\setupDirection@}#1\restore\restore - \xy@{end of 2-cell}\xysaveMinMax@ }}% - -\xydef@\xysaveMinMax@{\edef\tmp@{\endgroup - \noexpand\ifdim\X@max<\the\X@max \X@max=\the\X@max\noexpand\fi - \noexpand\ifdim\X@min>\the\X@min \X@min=\the\X@min\noexpand\fi - \noexpand\ifdim\Y@max<\the\Y@max \Y@max=\the\Y@max\noexpand\fi - \noexpand\ifdim\Y@min>\the\Y@min \Y@min=\the\Y@min\noexpand\fi - }\tmp@ } -\DOCMODE) - -\DOCMODE( -\xylet@\twocellPATH=\twocellpath -\xydef@\aftertwo@CELL{\let\twocellPATH=\twocellpath \def\aftertwoCELL{}} -\xydef@\aftertwoCELL{} -\DOCMODE) - - It remains to collect everything together and place it on the queue. - -\DOCMODE( -\xydef@\twocell@@@@#1!!!{\xy@{twocell #1}{\twocell@@#1!!!}} -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\subsection{2-cells in general \Xy-pictures} -??=[standard] -Two-cells can also be set directly within any \Xy-picture, without the -matrix feature, using either |\drop| or |\connect|. - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\DOCMODE( -\let\xystatus=\xystatus@ -\xydef@\twocell{\hbox\bgroup\@twocell} -\xydef@\uppertwocell{\hbox\bgroup\@uppertwocell} -\xydef@\lowertwocell{\hbox\bgroup\@lowertwocell} -\xydef@\compositemap{\hbox\bgroup\@compositemap} - -\xydef@\twocelll#1#{\hbox\bgroup\xy@\save\save@\@twocelll{#1}} -\xydef@\@twocelll#1#2{% - \afterPOS{\@twocelll@\xyFN@\twocell@#1{#2}}} - -\xydef@\uppertwocelll#1#{\hbox\bgroup\xy@\save\save@\@uppertwocelll{#1}} -\xydef@\@uppertwocelll#1#2{% - \afterPOS{\@twocelll@\xyFN@\uppertwocell@#1{#2}}} - -\xydef@\lowertwocelll#1#{\hbox\bgroup\xy@\save\save@\@lowertwocelll{#1}} -\xydef@\@lowertwocelll#1#2{% - \afterPOS{\@twocelll@\xyFN@\lowertwocell@#1{#2}}} - -\xydef@\compositemapp#1#{\hbox\bgroup\xy@\save\save@\@compositemapp{#1}} -\xydef@\@compositemapp#1#2{% - \afterPOS{\@twocelll@\xyFN@\compositemap@#1{#2}}} -% -\xydef@\@twocelll@{% -% \idfromc@{@c}\swap@\idfromc@{@p}\swap@ - \expandafter\edef\csname Q@@c\endcsname{\cfromthec@}\swap@ - \expandafter\edef\csname Q@@p\endcsname{\cfromthec@}\swap@ - \let\twocellPATH=\twocell@path -% \def\aftertwoCELL{\twocell@DONE}} - \def\aftertwoCELL{\twocell@DONE \xy@\restore \leave@ -% \cfromid@{@c}\no@@ \xystatus@{end: } - }} - -\xydef@\@twocell#1{\DN@{\@twocell@\twocell@}\xyFN@\next@[#1]} -\xydef@\@uppertwocell#1{\DN@{\@twocell@\uppertwocell@}\xyFN@\next@[#1]} -\xydef@\@lowertwocell#1{\DN@{\@twocell@\lowertwocell@}\xyFN@\next@[#1]} -\xydef@\@compositemap#1{\DN@{\@twocell@\compositemap@}\xyFN@\next@[#1]} -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\begin{code} -\def\myPOS#1{\POS}\def\goVia#1{% - \afterPOS{\connect#1\myPOS}} -\xy - *+{A}="A",+<1cm,1.5cm>*+{B}="B", - +<2.0cm,0pt>*+{C}="C", - +<1cm,-1.5cm>*+{D}="D", -"A";\goVia{\uppertwocell^\alpha{}}"B"{} -;\goVia{\twocell^\zeta_\xi{\gamma}}"C"{} -;\goVia{\compositemap{}}"D"{}, -"A";\goVia{\lowertwocell{}}"D"{} -\endxy -\end{code} - -\displaycode -%\begin{figure}[hbt] -$$\docode$$ -%??=[f.xypic] -%\caption{2-cells in \protect\Xy-pictures} -%\end{figure} - -\begin{code} -\xy *+{A}="A",+<1cm,1.5cm>*+{B}="B", - +<2cm,0pt>*+{C}="C", - +<1cm,-1.5cm>*+{D}="D", -"A";"B",{\uppertwocell^\alpha{}}, -"B";"C",{\twocell^\zeta_\xi{\gamma}}, -"C"; \afterPOS{\drop\compositemap{}}"D" -\POS "A"; - \afterPOS{\drop\lowertwocell{}}"D" -\endxy -\end{code} - -The code shown is a compact way to place a chain -of 2-cells within a picture. -It illustrates a standard technique for using -|\afterPOS| to find a <pos> to be used for part of -a picture, then subsequently reuse it. -Also it is possible to use |\drop| or <decor>s -to specify the 2-cells, giving the same picture. - -\displaycode - -The |\connect| variant is usually preferable -as this maintains the size of the object at $c$, -while the |\drop| variant leaves -a rectangular object having $p$ and $c$ on opposite sides. - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - This is used outside of diagrams. - -\DOCMODE( -\xydef@\@twocell@#1{\ifx\next[\DN@[{\toks@={#1}\xyFN@\@@twocell@}% - \else\DN@{#1{}}\fi -%% -% \idfromc@{@c}\swap@\idfromc@{@p}\swap@ - \expandafter\edef\csname Q@@c\endcsname{\cfromthec@}\swap@ - \expandafter\edef\csname Q@@p\endcsname{\cfromthec@}\swap@ - \let\twocellPATH=\twocell@path - \def\aftertwoCELL{\twocell@DONE}\next@} -\DOCMODE) - -This hack is necessary, since |\DN@[##1]{#1##1}| will strip braces. - -\DOCMODE( -\xydef@\@@twocell@{\ifx\next\bgroup\DN@##1]{\the\toks@{##1}}% - \else\DN@##1]{\the\toks@##1}\fi\next@} -\DOCMODE) - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\TODO: - These are supposed to allow |\dir\...twocell{...}| to work. - At present it seems to be impossible to do this. - -\DOCMODE( -% \expandafter\xydefcsname@\expandafter{\codeof\twocell}{\@twocell} -% \expandafter\xydefcsname@\expandafter{\codeof\uppertwocell}{\@uppertwocell} -% \expandafter\xydefcsname@\expandafter{\codeof\lowertwocell}{\@lowertwocell} -% \expandafter\xydefcsname@\expandafter{\codeof\compositemap}{\@compositemap} -%% \DN@{\twocell}% -%% \expandafter\def\csname*dir@@\codeof\next@ @\endcsname{\@twocell} -%% \DN@{\uppertwocell}% -%% \expandafter\def\csname*dir@@\codeof\next@ @\endcsname{\@uppertwocell} -%% \DN@{\lowertwocell}% -%% \expandafter\def\csname*dir@@\codeof\next@ @\endcsname{\@lowertwocell} -%% \DN@{\compositemap}% -%% \expandafter\def\csname*dir@@\codeof\next@ @\endcsname{\@compositemap} -\DOCMODE) - -...since the contents of |{..}| is variable. - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - - Finish off the box, set up the object size, - establish the |\Drop@@| and |\Connect@@| methods. - -\DOCMODE( -\xydef@\twocell@DONE{% - \edef\tmp@{\egroup \X@min=\the\X@min \X@max=\the\X@max - \Y@min=\the\Y@min \Y@max=\the\Y@max}\tmp@ - \L@c=\X@c \advance\L@c-\X@min \R@c=\X@max \advance\R@c-\X@c - \D@c=\Y@c \advance\D@c-\Y@min \U@c=\Y@max \advance\U@c-\Y@c - \ht\z@=\U@c \dp\z@=\D@c \dimen@=\L@c \advance\dimen@\R@c \wdz@=\dimen@ - \computeLeftUpness@ -% -\setboxz@h{\kern-\X@p \raise-\Y@c\boxz@ }% -\dimen@=\L@c \advance\dimen@\R@c \wdz@=\dimen@ \ht\z@=\U@c \dp\z@=\D@c -% - \Edge@c={\rectangleEdge}\Invisible@false \Hidden@false - \edef\Drop@@{\noexpand\drop@Twocell - \noexpand\def\noexpand\Leftness@{\Leftness@}% - \noexpand\def\noexpand\Upness@{\Upness@}}% - \edef\Connect@@{\noexpand\connect@Twocell - \noexpand\ifdim\X@max<\the\X@max \X@max=\the\X@max\noexpand\fi - \noexpand\ifdim\X@min>\the\X@min \X@min=\the\X@min\noexpand\fi - \noexpand\ifdim\Y@max<\the\Y@max \Y@max=\the\Y@max\noexpand\fi - \noexpand\ifdim\Y@min>\the\Y@min \Y@min=\the\Y@min\noexpand\fi }}% -\DOCMODE) - - modified |\Drop@@| and |\Connect@@| - -\DOCMODE( -\xydef@\drop@Twocell{\boxz@ } - -\xydef@\connect@Twocell{% - \setboxz@h{\kern\X@p \raise\Y@c\box\lastobjectbox@ }% - \wdz@=\z@ \ht\z@=\z@ \dp\z@=\z@ \Drop@@ } -\DOCMODE) - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -|\twocell@@| is the main switching engine, taking 9 parameters determining - which pieces to set and where to position them. This includes - curvature of the squines, whether to draw two squines - or only one, or to use straight lines, - whether to have a central Arrow and its orientation, - contants of labels and their positions. - - The current p and c are the extents of the connection - these are stored as |"@p"| and |"@c"| for repeated use; - -\begin{defs1} -\begin{tabular}{c l} - |#1| & determines location of control point |"@m"|\cr - |#2| & location of |=>|, as multiple of |\xydashl@| from |"@m"|\cr - |#3| & location of |_| label (source arrow)\cr - |#4| & location of |^| label (target arrow)\cr - |#5| & flag for how many squines to draw \& which tips\cr - |#6| & label for source arrow\cr - |#7| & label for target arrow\cr - |#8| & label for |=>| (2-cell morphism)\cr - |#9| & determines orientation of 2-cell \cr -\end{tabular} -\end{defs1} - -The following tokens may appear as parameters in |#9|: -|!|, |^|, |_|, |=|, |A|, |V|, |H| - -\DOCMODE( -\xywarnifdefined\@mod@ -\xywarnifdefined\Arrowtok@ - -\xydef@\twocell@@#1#2#3#4#5#6#7#8#9!!!{% - \def\@mod@{@}\DN@{#9}% - \ifx #9!\def\Arrowtok@{@}\else\ifx #9A\def\Arrowtok@{^}% - \else\ifx #9V\def\Arrowtok@{_}\else\ifx #9H\def\Arrowtok@{=}% - \else\def\@mod@{\relax}% - \ifx #5/\def\Arrowtok@{@}\else\ifx #5b\def\Arrowtok@{@}% - \else\ifx #5B\def\Arrowtok@{@}\else\ifx #5@\def\Arrowtok@{@}% - \else\def\Arrowtok@{#9}% - \fi\fi\fi\fi\fi\fi\fi\fi - \addEQ@\ifx #9\def\Arrowtok@{=}\fi - \DN@{\omit}\ifx\next@\Arrowtok@\def\Arrowtok@{}\else - \edef\Arrowtok@{\codeof\Arrowtok@}\fi - \save@ \idfromc@{@c}\swap@\idfromc@{@p}\swap@ - \cfromid@{@c}\no@@ -% - \ifdim \X@c<\X@p \X@min=\X@c \X@max=\X@p \else \X@min=\X@p \X@max=\X@c \fi - \ifdim \Y@c<\Y@p \Y@min=\Y@c \Y@max=\Y@p \else \Y@min=\Y@p \Y@max=\Y@c \fi -% - \Calong@@{.5}\idfromc@{@m}\idfromc@{@m1}\idfromc@{@m2}% -% - \ifx #5t\relax - \enter@{\cplusthec@\pfromthep@}% - \enter@\DirectionfromtheDirection@ \begingroup\aboveDirection@ \xydashl@ - \DN@{#1}\ifx\next@\empty\dimen@=\z@\else\dimen@=#1\p@\fi - \ifdim\dimen@=\z@ \DN@{\vfromslide@i{\xydashl@}@}\relax - \else\DN@{\vfromslide@i{#1\xydashl@}@}\fi \next@ - \czeroEdge@ \leave@ \no@@ \drop@{+}{}\idfromc@{@m1}% - \DN@{#1}\ifx\next@\empty\DN@{\no@@}\else\DN@{\connect@{\dir}{-}}\fi - \else - \DN@{#1}\ifx\next@\empty\dimen@=\z@\else\dimen@=#1\p@\fi - \ifdim\dimen@=\z@ \enter@{\cplusthec@\pfromthep@}% - \enter@\DirectionfromtheDirection@ \begingroup\aboveDirection@\xydashl@ - \vfromslide@i{\xydashl@}@\czeroEdge@ \leave@ \idfromc@{@m1}% - \cfromid@{@p}\swap@\cfromid@{@c}% - \DN@{#1}\ifx\next@\empty\DN@{\no@@}\else\DN@{\connect@{\dir}{-}}\fi - \else \DN@{\enter@\cplusthec@ - \enter@\DirectionfromtheDirection@ \begingroup\aboveDirection@ \xydashl@ - \vfromslide@i{#1\xydashl@}@\czeroEdge@ \leave@ - \idfromc@{@m1}\cfromid@{@p}\swap@\cfromid@{@c}% - \edef\next@{\codeof\ucurveObject@}% - \ifx\next@\empty\DN@{\connect@\crv{"@m1"}}% - \else - \DNii@####1{\connect@\crv{####1}}\expandafter\DN@\expandafter{% - \expandafter\nextii@\expandafter{\ucurveObject@"@m1"}}% - \fi \next@ }% -%% \ifx\next@\empty\def\ucurveObject@{.}\fi -%% \enter@\cfromthec@\sinit@\cfromid@{@m1}\senter@\leave@ -%% \expandafter\connect@\expandafter\crvs\expandafter{\ucurveObject@}% -%% \sinit@\sleave@ }% - \fi - \fi \next@ -% - \DN@{#1}\ifx\next@\empty\relax\else - \if\@mod@ @\relax - \enter@\pfromthep@ \Creset@@ - \ifx #5t\relax - \PLACEedgec@ \PLACEedgep@ \def\PLACEf@{{.5}}% - \else \def\next@{\crvreset@}% - \ifx\next@\Creset@@ - \gettwocelledges@ \edef\PLACEf@{{\expandafter\removePT@\the\dimen@}}% - \else \PLACEedgec@ \PLACEedgep@ \def\PLACEf@{{.5}}\fi - \fi - \expandafter\Calong@@\PLACEf@ \czeroEdge@ \leave@ - \edef\tmp@{\codeof\modmapobject@}% - \ifx\tmp@\empty \DN@{\drop@{\dir}{|}}% - \else \DNii@##1##{\drop@{##1}}% - \DN@{\expandafter\nextii@\modmapobject@{}}% - \fi \next@ - \fi\fi -% - \DN@{#6}\ifx\next@\empty\DN@{\relax}\else - \DNii@{{}}\ifx\next@\nextii@\DN@{\relax}\else - \ifx @#3\relax\DN@{\relax}\else - \DN@{\enter@\pfromthep@ \Creset@@ - \Calong@@{.5}\czeroEdge@ \leave@ - \enter@\cplusthec@ - \enter@\DirectionfromtheDirection@\begingroup - \DN@{#1}\ifx\next@\empty\dimen@\z@\else\dimen@=#1\p@\fi - \ifdim\dimen@<\z@ \belowDirection@ \xydashl@ - \else \aboveDirection@ \xydashl@ \fi -% \vfromslide@i{#3\xydashl@}@\czeroEdge@ \leave@ -% \droptwocelllabel@{#6}}% - \dimen@=#3\p@ \if\@mod@ @\relax - \advance\dimen@\ifdim\dimen@<\z@-\fi.5\p@\fi - \edef\next@{\expandafter\removePT@\the\dimen@}% - \expandafter\vfromslide@i\expandafter{\next@\xydashl@}@\leave@ - \droptwocelllabel@{#6}}% - \fi\fi\fi \next@ -% -% - \DN@{#1}\ifx\next@\empty\relax\else - \ifx #5b\relax % tip at start only - \enter@ {\pfromthep@ }\Creset@@ \PLACEedgep@ - \Calong@@{0}\czeroEdge@ \leave@ - \edef\next@{\codeof\twocelltail@}% - \ifx\next@\empty \DN@{\dir{>}}% - \ifx\next@\twocellhead@\drop@{\dir}{<}% - \else - \reverseDirection@ \DNii@##1##{\drop@{##1}}% - \expandafter\nextii@\twocellhead@{}\reverseDirection@ - \fi - \else - \DNii@##1##{\drop@{##1}}\expandafter\nextii@\twocelltail@{}% - \fi - \else\ifx #5@\relax % no tips at all - \else % tip at end... - \enter@\pfromthep@ \Creset@@ \PLACEedgec@ - \Calong@@{1}\czeroEdge@ \leave@ - \edef\next@{\codeof\twocellhead@}% - \ifx\next@\empty\drop@{\dir}{>}% - \else - \DNii@##1##{\drop@{##1}}\expandafter\nextii@\twocellhead@{}% - \fi - \ifx #5B\relax % ... and also at start. - \enter@ {\pfromthep@ }\Creset@@ \PLACEedgep@ - \Calong@@{0}\czeroEdge@ \leave@ - \edef\next@{\codeof\twocelltail@}% - \ifx\next@\empty \DN@{\dir{>}}% - \ifx\next@\twocellhead@\drop@{\dir}{<}% - \else - \reverseDirection@\DNii@##1##{\drop@{##1}}% - \expandafter\nextii@\twocellhead@{}\reverseDirection@ - \fi - \else - \DNii@##1##{\drop@{##1}}\expandafter\drop\twocelltail@{}% - \fi - \else\ifx #5/\relax - \else \edef\next@{\codeof\twocelltail@}% - \ifx\next@\empty\relax\else - \enter@\pfromthep@ \Creset@@ \PLACEedgep@ - \Calong@@{0}\czeroEdge@ \leave@ - \DNii@##1##{\drop@{##1}}\expandafter\nextii@\twocelltail@{}% - \fi\fi\fi - \fi\fi\fi -% - \cfromid@{@p}\swap@\cfromid@{@c}\no@@ \cfromid@{@m}% - \ifx #5t\relax - \idfromc@{@m2}\cfromid@{@m1}\swap@ \cfromid@{@c}\no@@ - \DN@{#1}\ifx\next@\empty\DN@{\no@@}\else\DN@{\connect@{\dir}{-}}\fi - \else\ifx #5o\relax - \idfromc@{@m2}\DN@{}% - \else % second curved arrow - \DN@{#1}\ifx\next@\empty\dimen@=\z@\else\dimen@=#1\p@\fi - \ifdim\dimen@=\z@ - \enter@{\cplusthec@\pfromthep@}% - \enter@\DirectionfromtheDirection@ \begingroup \belowDirection@\xydashl@ - \vfromslide@i{\xydashl@}@\czeroEdge@ \leave@ \idfromc@{@m2}% - \DN@{\cfromid@{@p}\swap@\cfromid@{@c}\no@@}% - \else \DN@{\enter@\cplusthec@ - \enter@\DirectionfromtheDirection@ \begingroup \belowDirection@ \xydashl@ - \vfromslide@i{#1\xydashl@}@\czeroEdge@ \leave@ - \idfromc@{@m2}\cfromid@{@p}\swap@\cfromid@{@c}% - \edef\next@{\codeof\dcurveObject@}% - \ifx\next@\empty\DN@{\connect@\crv{"@m2"}}% - \else - \DNii@####1{\connect@\crv{####1}}\expandafter\DN@\expandafter{% - \expandafter\nextii@\expandafter{\dcurveObject@"@m2"}}% - \fi \next@ }\fi -%% \enter@\cfromthec@\sinit@\cfromid@{@m2}\senter@\leave@ -%% \expandafter\connect@\expandafter\crvs\expandafter{\dcurveObject@}% -%% \sinit@\sleave@ -%% }\fi - \fi\fi \next@ -% - \DN@{#1}\ifx\next@\empty\relax\else \ifx #5o\relax\else - \if\@mod@ @\DN@{\enter@\pfromthep@ \Creset@@ - \ifx #5t\relax - \PLACEedgec@ \PLACEedgep@ \def\PLACEf@{{.5}}% - \else \def\next@{\crvreset@}% - \ifx\next@\Creset@@ - \gettwocelledges@ \edef\PLACEf@{{\expandafter\removePT@\the\dimen@}}% - \else \PLACEedgec@ \PLACEedgep@ \def\PLACEf@{{.5}}\fi - \fi - \expandafter\Calong@@\PLACEf@ \czeroEdge@ \leave@ - \edef\tmp@{\codeof\modmapobject@}\ifx\tmp@\empty\DN@{\drop@{\dir}{|}}% - \else \DNii@####1####{\drop@{####1}}% - \DN@{\expandafter\nextii@\modmapobject@{}}\fi - \next@ }\else\DN@{\relax}\fi - \next@ \fi\fi -% - \DN@{#7}\ifx\next@\empty\DN@{\relax}\else - \DNii@{{}}\ifx\next@\nextii@\DN@{\relax}\else - \ifx @#4\relax\DN@{\relax}\else - \DN@{\enter@\pfromthep@ \Creset@@ - \Calong@@{.5}\czeroEdge@ \leave@ - \enter@\cplusthec@ - \enter@\DirectionfromtheDirection@ \begingroup - \DN@{#1}\ifx\next@\empty\dimen@\z@ \else\dimen@=#1\p@\fi - \ifx #5t\relax \ifdim\dimen@<\z@ \belowDirection@ \xydashl@ - \else \aboveDirection@ \xydashl@ \fi - \else \ifdim\dimen@<\z@ \aboveDirection@ \xydashl@ - \else \belowDirection@ \xydashl@ \fi - \fi \dimen@=#4\p@ \if\@mod@ @\relax - \advance\dimen@\ifdim\dimen@<\z@-\fi.5\p@\fi - \edef\next@{\expandafter\removePT@\the\dimen@}% - \expandafter\vfromslide@i\expandafter{\next@\xydashl@}@\leave@ - \droptwocelllabel@{#7}}% - \fi\fi\fi \next@ -% - \DN@{#1}\ifx\next@\empty\relax\else - \ifx #5o\relax - \else\ifx #5b\relax % tip at start only - \enter@ {\pfromthep@ }\Creset@@ \PLACEedgec@ - \Calong@@{1}\czeroEdge@ \leave@ - \edef\next@{\codeof\twocelltail@}% - \ifx\next@\empty \DN@{\dir{>}}% - \ifx\next@\twocellhead@\drop@{\dir}{>}% - \else - \DNii@##1##{\drop@{##1}}\expandafter\nextii@\twocellhead@{}% - \fi - \else - \DNii@##1##{\drop@{##1}}\expandafter\drop\twocelltail@{}% - \fi - \else\ifx #5/\relax - \enter@{\pfromthep@}\Creset@@ \PLACEedgep@ - \Calong@@{0}\czeroEdge@ \leave@ - \edef\next@{\codeof\twocelltail@}% - \ifx\next@\empty \DN@{\dir{>}}% - \ifx\next@\twocellhead@\drop@{\dir}{<}% - \else - \reverseDirection@\DNii@##1##{\drop@{##1}}% - \expandafter\nextii@\twocellhead@{}\reverseDirection@ - \fi - \else - \DNii@##1##{\drop@{##1}}\expandafter\nextii@\twocelltail@{}% - \fi - \else\ifx #5@\relax % no tips at all - \else % tip at end... - \enter@\pfromthep@ \Creset@@ \PLACEedgec@ - \Calong@@{1}\czeroEdge@ \leave@ - \edef\next@{\codeof\twocellhead@}% - \ifx\next@\empty\drop@{\dir}{>}% - \else - \DNii@##1##{\drop@{##1}}\expandafter\nextii@\twocellhead@{}% - \fi - \ifx #5B\relax % ... and also at start. - \enter@ {\pfromthep@ }\Creset@@ \PLACEedgep@ - \Calong@@{0}\czeroEdge@ \leave@ - \edef\next@{\codeof\twocelltail@}% - \ifx\next@\empty\DN@{\dir{>}}% - \ifx\next@\twocellhead@\drop@{\dir}{<}% - \else - \reverseDirection@\DNii@##1##{\drop@{##1}}% - \expandafter\nextii@\twocellhead@{}\reverseDirection@ - \fi - \else - \DNii@##1##{\drop@{##1}}\expandafter\nextii@\twocelltail@{}% - \fi - \else - \edef\next@{\codeof\twocelltail@}% - \ifx\next@\empty\relax\else - \enter@ {\pfromthep@ }\Creset@@ \PLACEedgep@ - \Calong@@{0}\czeroEdge@ \leave@ - \DNii@##1##{\drop@{##1}}\expandafter\nextii@\twocelltail@{}% - \fi\fi - \fi\fi\fi - \fi\fi -% -% the Arrow -% - \DN@{#1}\ifx\next@\empty\dimen@=\z@\else\dimen@=#1\p@\fi - \ifdim\dimen@<\z@ \cfromid@{@m2}\swap@\cfromid@{@m1}% - \else \cfromid@{@m1}\swap@\cfromid@{@m2}% - \fi \no@@ \cfromid@{@m}% -% - \ifx\Arrowtok@\empty -% - \else\DN@{_}\edef\next@{\codeof\next@}\ifx\next@\Arrowtok@ - \enter@{\pfromthep@ \cplusthec@}\dimen@=#2\xydashl@ - \enter@\DirectionfromtheDirection@ \begingroup - \expandafter\vfromslide@i\expandafter{\the\dimen@}@\czeroEdge@ - \leave@ \idfromc@{@m}% - \DNii@##1##{\drop@{##1}}\expandafter\nextii@\Arrowobject@{}% -% \drop@{\dir}{=>}% -% - \else\DN@{^}\edef\next@{\codeof\next@}\ifx\next@\Arrowtok@ - \DN@{_}\edef\Arrowtok@{\codeof\next@}% - \enter@{\pfromthep@ \cplusthec@}\dimen@=#2\xydashl@ - \enter@\DirectionfromtheDirection@ \begingroup - \expandafter\vfromslide@i\expandafter{\the\dimen@}@\czeroEdge@ - \leave@ \idfromc@{@m}\reverseDirection@ - \DNii@##1##{\drop@{##1}}\expandafter\nextii@\Arrowobject@{}% -% \drop@{\dir}{=>}% -% - \else \DN@{=}\edef\next@{\codeof\next@}\ifx\next@\Arrowtok@ - \enter@{\pfromthep@ \cplusthec@}% - \dimen@=#2\xydashl@ \advance\dimen@\xydashl@ - \enter@\DirectionfromtheDirection@ \begingroup - \expandafter\vfromslide@i\expandafter{\the\dimen@}@\czeroEdge@ - \leave@ \idfromc@{@m2}% - \cfromid@{@m}% - \enter@{\pfromthep@ \cplusthec@}% - \dimen@=#2\xydashl@ \advance\dimen@-\xydashl@ - \enter@\DirectionfromtheDirection@ \begingroup - \expandafter\vfromslide@i\expandafter{\the\dimen@}@\czeroEdge@ - \leave@ \idfromc@{@m1}% - \cfromid@{@m2}\swap@\cfromid@{@m1}\connect@{\dir 2}{-}% - \fi\fi\fi\fi -% -% label on the Arrow -% - \DN@{#8}\ifx\next@\empty\DN@{}\else\DN@{% - \ifx\Arrowtok@\empty - \Calong@@{.5}% - \else\DN@{=}\edef\next@{\codeof\next@}\ifx\next@\Arrowtok@ - \Calong@@{.5}% - \else\DN@{_}\edef\next@{\codeof\next@}\ifx\next@\Arrowtok@ - \cfromid@{@m}% - \fi\fi\fi - \enter@\cplusthec@ - \enter@\DirectionfromtheDirection@ \begingroup \aboveDirection@\xydashl@ - \ifx\Arrowtok@\empty - \def\tmp@{0pt}% - \else\DN@{=}\edef\next@{\codeof\next@}\ifx\next@\Arrowtok@ - \def\tmp@{\xydashl@}% - \else\DN@{_}\edef\next@{\codeof\next@}\ifx\next@\Arrowtok@ - \def\tmp@{1.2\xydashl@}% - \else\def\tmp@{0pt}% - \fi\fi\fi - \expandafter\vfromslide@i\expandafter{\tmp@}@\czeroEdge@ \leave@ - \droptwocelllabel@{#8}% - }\fi \next@ - \leave@ }% -\DOCMODE) - -These are used to establish the location for -the module-map indicator, giving best aesthetic appeal. -It finds the location whose parameter value is -the average of half-way along the complete curve and -the average of parameter values at the the edges. - -\DOCMODE( -\xydef@\gettwocelledges@{% - \bgroup \the\crvpts@ - \edef\next@{\edges@}% - \expandafter\gettwocelledges@@\next@ } - -\xydef@\gettwocelledges@@#1;#2,#3;#4,{% - \dimen@=#2\advance\dimen@-#4\relax - \advance\dimen@ 2\p@ \divide\dimen@ by4 \relax - \edef\next@{\egroup\dimen@=\the\dimen@ }\next@}% -\DOCMODE) - -\DOCMODE2%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\paragraph*{The end \& Log}\leavevmode - -DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -\DOCMODE( -\xyendinput - -% $Log: xy2cell.doc,v $ -% Revision 3.3 1996/12/18 14:21:23 ross -% Ross's version -% -% Revision 3.3.1.1 1996/12/18 08:49:34 ross -% *** empty log message *** -% -% Revision 3.1 1995/09/05 20:36:33 ross -% Release! -% -% Revision 3.0 1995/07/07 20:13:19 ross -% Major release w/new User's Guide! -% -% Revision 2.14 1995/07/05 22:11:25 kris -% Buglets... -% -% Revision 2.13 1995/07/04 15:04:51 ross -% Ready for release of v3. -% -% Revision 2.12 1994/10/25 03:01:14 ross -% Final 3beta release [bug fixes & AMS-LaTeX fitting]. -% -% Revision 2.10 1994/07/01 01:19:46 ross -% removed undefined references -% -% Revision 2.9 1994/06/09 12:51:27 ross -% Release 3beta. -% -% NEW for version 2.9 based on unreleased code for version 2.6+. -\DOCMODE) - -\DOCMODE3%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%%% - -% Tell Emacs that this is a LaTeX document and how it is formatted: -% Local Variables: -% mode:latex -% fill-column:77 -% fill-prefix:"" -% End: |